Study Guide for Module 18—Nuclear Chemistry Assignment: Chapter 18 in Chemistry, ... Structure of...

Chemistry 1020, Module 18 Name

Study Guide for Module 18—Nuclear Chemistry

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Reading Assignment: Chapter 18 in Chemistry, 6h Edition by Zumdahl.

Guide for Your Lecturer:

✔ 1. Review From Chemistry 1010: Structure of the Atom2. Modes of Radioactive Decay3. Comparison of Nuclear and Chemical Reactions

✔ 4. Balancing Equations for Nuclear Reactions5. Stability of Nuclides

✔ 6. Stability of Nuclides: Predicting Most Probable Modes of Decay✔ 7. Binding Energy 8. Fission and Fusion✔ 9. Kinetics of Radioactive Decay, Radioactive Dating 10. Biological Effects of Ionizing Radiation

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HomeworkNote: ✔ indicates problems to be stressed on drill quizzes and hour exams.✔✔✔■Review From Chemistry 1010: Structure of the Atom1. All modules which we have covered previously in both Chemistry 1010 and 1020 considered traditional topics in

chemistry. In this, the final module in 1020, we study an area in which there is overlap between chemistry andphysics. We call this area nuclear chemistry (and physicists probably call it nuclear physics). As the name implieswe are more concerned with the nuclei of atoms in nuclear chemistry than with the electrons. Therefore, we willbegin with a review of the components of the atom, their location in the atom, etc.

a) Complete the following table regarding the components of the atom. (p. 53, inside back cover of text)particle | approx. mass in grams |approx. mass in amu | charge in coulombs |relative charge |electron | | | | | | | | | |proton | | | | | | | | | |neutron | | | | | | | | | |

b) Answer the following questions.A. Give a general description of the manner in which electrons, protons, and neutrons are organized in the

atom. (p. 53-4)

-----------------------------------------------------------------------------------------------------------------------------------------------B. Where is the positive charge in an atom located? (p. 53)

-----------------------------------------------------------------------------------------------------------------------------------------------C. Where is most of the mass of an atom? (p. 54)

-----------------------------------------------------------------------------------------------------------------------------------------------D. Where are the neutrons in an atom? (p. 53)

-----------------------------------------------------------------------------------------------------------------------------------------------E. What is the approximate radius of an atom? (p. 53)

Xavier University of Louisiana 373

Chemistry 1020, Module 18

■Review From Chemistry 1010: Structure of the Atom (continued)1b) F. If an atom were the size of the SuperDome, approximately how large would its nucleus be? (About the

size of a green pea.)

-----------------------------------------------------------------------------------------------------------------------------------------------G. Where is the negative charge in an atom? (p. 53)

-----------------------------------------------------------------------------------------------------------------------------------------------H. How does a cation differ from the atom to which it is related? (p. 57)

-----------------------------------------------------------------------------------------------------------------------------------------------I. How does an anion differ from the atom to which it is related? (p. 58)

-----------------------------------------------------------------------------------------------------------------------------------------------c) Define nucleus (p. 53)

-----------------------------------------------------------------------------------------------------------------------------------------------d) Define atomic number (p. 54)

-----------------------------------------------------------------------------------------------------------------------------------------------e) Define mass number (p. 54)

-----------------------------------------------------------------------------------------------------------------------------------------------f) Define nuclide (p. 878)

-----------------------------------------------------------------------------------------------------------------------------------------------g) Define isotopes (p. 878)

-----------------------------------------------------------------------------------------------------------------------------------------------h) Fill in the table for the chemical species below.

| | Number | Number | Number |approx. | Charge on | Mass |Atomic |isotope | | of protons |of electrons |of neutrons |mass | nucleus | number |number | S. | | | | 38-16 = | ≈38 | | | |

|38S+ | 16 | 15 | 22 | amu | +16 | 38 | 16 | 39S+

| | | | | | | | | A. | | | | | | | | |

|45Ca+ | | | | | | | | | | | | | | | | | B. | | | | | | | | |

|34P2- | | | | | | | | | | | | | | | | | C. | | | | | | | | |

|28Si3+ | | | | | | | | | | | | | | | | | D. | | | | | | | | |

|122Sn2-| | | | | | | | | | | | | | | | |

374 Xavier University of Louisiana


■Modes of Radioactive Decay2a) All isotopes of elements with an atomic number greater than 83 and many isotopes of elements with lower

atomic numbers are unstable. I.e. undergo spontaneous decay to form other elements. Such elements are said tobe “radioactive.” Define radioactivity. (The spontaneous decay of an unstable nuclide by a first-order process.)

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b) Radioactive decay is usually accompanied by the emission of a one or more types of radiation. List the fourtypes of nuclear radiation which can be emitted as a result of radioactive decay. Describe each by completing thetable below . (pp. 880-1Name of radiation |Symbol for rad |Mass of particle |Charge on particle |Other name (if any) 1) | | | | | | | | 2) | | | | | | | | 3) | | | | | | | | 4) | | | | | | | |

c) List and describe another way in which a nuclide might decay. (pp. 881) Name of radiation |Description of decay mode 1) | |

d) What is the difference between a positron and an electron? (They both have the same mass, about 1/1800amu, but they have opposite charges. The charge of an electron is -1 and the charge of a positron is+1.)

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e) Write the mass numbers and atomic numbers on the symbols for each of the following particles.

• α • β− • γ • β+

• n • p • e-

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■Comparison of Nuclear and Chemical Reactions3. Nuclear reactions differ significantly from chemical ones. List four ways in which they differ. (1. The

energy changes in nuclear reactions are much larger than those in chemical reactions. 2. Oneelement cannot be changed into another in a chemical reactions but can in a nuclear one. 3. Differentisotopes of an element behave in the same manner in chemical reactions but not in nuclear ones. 4.The chemical state of an element affects the manner in which it reacts in a chemical reaction but not ina nuclear one.)-1)

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✔✔✔■Balancing Equations for Nuclear Reactions4. Complete and balance the indicated nuclear equation. (pp. 881-2, In nuclear reactions, balance protons,

neutrons, and electrons (if not in an atom) by balancing mass # and atomic #. Ignore electrons in theatom unless they are directly involved in the reaction such as in electron-capture (aka K-capture).)

a) S. 56Fe + e- ➝ ?

56 0 56 omass number = 56 (from Fe) + 0 (from e- ) = 56

Fe + e- ➝ Mn26 -1 25 oatomic number = 26 (from Fe) + -1 (from e- ) = 25

-----------------------------------------------------------------------------------------------------------------------------------------------A. 252Cf + 10B ➝ 3 n + ?

-----------------------------------------------------------------------------------------------------------------------------------------------B. 122I ➝ 122Xe + ?

-----------------------------------------------------------------------------------------------------------------------------------------------C. 149Eu + p ➝ 2 p +?

-----------------------------------------------------------------------------------------------------------------------------------------------D. 40K ➝ positron + ?

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✔✔✔■Balancing Equations for Nuclear Reactions (continued)4a) E. 235U + n ➝ 138Ba + 2 n + ?

-----------------------------------------------------------------------------------------------------------------------------------------------F. 2H + 3He ➝ 4He + ?

-----------------------------------------------------------------------------------------------------------------------------------------------G. 59Fe ➝ e- + ?

-----------------------------------------------------------------------------------------------------------------------------------------------H. 86Se ➝ alpha + ?

-----------------------------------------------------------------------------------------------------------------------------------------------I. 234Th + n ➝ ? + 3 n + alpha

-----------------------------------------------------------------------------------------------------------------------------------------------b) Define chain reaction with respect to radioactive decay. (A series of reactions in which one radioactive

nuclide decays to produce a second radioactive nuclide, the second decays to produce a thirdradioactive nuclide, etc. The process continues until a stable nuclide is formed.)

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c) Write balanced equations for each step in the following radioactive–decay chain reactions. (pp. 882)S. 238U first emits an alpha particle, then a beta, and finally a second beta.

238 4 234 U ➝ He2+ + Th 92 2 90

---------------------------------------------------------- 234 0 234 Th ➝ e- + Pa 90 -1 91

---------------------------------------------------------- 234 0 234 Pa ➝ e- + U 91 -1 92

-----------------------------------------------------------------------------------------------------------------------------------------------A. 222Rn first emits an alpha, then a gamma, and finally a beta.



✔✔✔■Balancing Equations for Nuclear Reactions (continued) 4c) B. 232Th first emits an alpha, then a beta, another beta, and finally an alpha.

----------------------------------------------------------------------------------------------------------------------------------------------- C. 237Np first emits an alpha, then a beta, and finally an alpha.

-----------------------------------------------------------------------------------------------------------------------------------------------D. 238U first emits a positron, then an alpha particle, and finally another alpha particle.

-----------------------------------------------------------------------------------------------------------------------------------------------E. 232U first emits a beta particle, then an alpha particle, and finally a second beta.

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■Stabil i ty of Nuclides5a) The theory which attempts to explain why certain nuclides are stable and others are not is much too complicated

to consider in General Chemistry. However, there are some empirical conclusions which can be reached byanalyzing the distribution of stable nuclides. Define empirical.

-----------------------------------------------------------------------------------------------------------------------------------------------b) State four empirical conclusions which can be made regarding which nuclides are stable. (1. All nuclides with

84 or more protons are unstable with respect to radioactive decay. 2. Light nuclides are stable whenthe neutron/proton ratio is “1”. However, for heavier elements, the neutron/proton ratio required forstability is greater than 1 and increases with atomic number. 3. Certain combinations of protons andneutrons seem to have special stability. For example, nuclides with even numbers of protons andneutrons are more often stable than those with odd numbers. 4. There are also specific numbers ofprotons or neutrons that produce especially stable nuclides. These so–called magic numbers are 2,8, 20, 28, 50, 82, and 126.)

•1)

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-----------------------------------------------------------------------------------------------------------------------------------------------•3)

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✔✔✔■Stabil i ty of Nuclides: Predicting Most Probable Modes of Decay6a) The shaded area on the graph below indicates the area where the stable nuclides fall when the number of neutrons

is plotted versus the number of protons.

120-

110-

100-

90-

80-

70-

60-

50-

40-

30-

20-

10-

0- • • • • • • • • • • •0 10 20 30 40 50 60 70 80 90 100 Number of protons

Number

of

neutrons

Ne n/p = 120

Fe n/p = 1.1556

•

•

•

•

Ag n/p = 1.28107

W n/p = 1.49184

On the basis of the sketch above, what generally happens to the n/p ratio as atomic number of stablenuclides increase?

----------------------------------------------------------------------------------------------------------------------------------------------b) What is the shaded area called? (The belt of stability.)

-----------------------------------------------------------------------------------------------------------------------------------------------c) Plots such as those in #a above can be used to predict the most probable manner in which an unstable nuclide

will decay. In general what kind of decay will an unstable nuclide undergo? (Any type which makes it movetoward the belt of stability.)

-----------------------------------------------------------------------------------------------------------------------------------------------d) When does alpha decay occur ? (Alpha decay occurs when the atomic number is greater than 83.)

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■Stabili ty of Nuclides: Predicting Most Probable Modes of Decay (continued)6d) Use arrows to show what happens to the n/p ratio (i.e. the position of a point on a graph of number of neutrons

versus number of protons) of a nuclide when it undergoes each of the following types of radioactive decay.Hint: See how each change affects oxygen-18.S. beta decay

12-

11-

10-

9-

8- • • • • • 6 7 8 9 10 Number of protons

#

neutrons

•

•

188O ➝ 189F + 0-1e-

#n = 10 9 so is -1#p = 8 9 so is +1Therefore, get change as shown above.

A. alpha decay

12-

11-

10-

9-


#

neutrons

B. positron decay

12-

11-

10-

9-


#

neutrons

C. e- capture or K-capture

12-

11-

10-

9-


#

neutrons



■Stabili ty of Nuclides: Predicting Most Probable Modes of Decay (continued)6e) Use the information from part a and d of this question to predict whether or not the indicated species will

undergo radioactive decay and, if so, how it will probably decay. Justify your answer.S. 20O

This nuclide contains 8 protons and 12 neutrons.When plotted on the graph of # n versus # p, it liesabove the belt of stability on the chart as seen to theright. That is, the nuclide is neutron rich. Weknow that it will decay so as to move back towardthe stable nuclides (i.e. toward the belt of stability).If we look at the types of possible decay in 6dabove, we can see that the only type of decaywhich will move it toward the belt of stability is betaemission. Therefore, we predict that 20O wouldprobably decay by beta emission.

120-

110-

100-

90-

80-

70-

60-

50-

40-

30-

20-

10-


Number

of

neutrons

•

-----------------------------------------------------------------------------------------------------------------------------------------------A. 137I 120-

110-

100-

90-

80-

70-

60-

50-

40-

30-

20-

10-


Number

of

neutrons

-----------------------------------------------------------------------------------------------------------------------------------------------B. 148Er 120-

110-

100-

90-

80-

70-

60-

50-

40-

30-

20-

10-


Number

of

neutrons

-----------------------------------------------------------------------------------------------------------------------------------------------C. 132Sm 120-

110-

100-

90-

80-

70-

60-

50-

40-

30-

20-

10-


Number

of

neutrons

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■Stabili ty of Nuclides: Predicting Most Probable Modes of Decay (continued)6e) Use the information from part a and d of this question to predict whether or not the indicated species will

undergo radioactive decay and, if so, how it will probably decay. Justify your answer.D. 35S 120-

110-

100-

90-

80-

70-

60-

50-

40-

30-

20-

10-


Number

of

neutrons

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E. 230Th 120-

110-

100-

90-

80-

70-

60-

50-

40-

30-

20-

10-


Number

of

neutrons

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■Binding Energy7a) At the beginning of Chemistry 1010, you learned the Law of Conservation of Mass and the Law of

Conservation of Energy. State those laws. (Law of Conservation of Mass: Mass is neither created nordestroyed when a chemical reaction occurs. Law of Conservation of Energy: Energy is neithercreated nor destroyed when a chemical reaction occurs.)•Law of Conservation of Mass:

•Law of Conservation of Energy:

-----------------------------------------------------------------------------------------------------------------------------------------------b) The Law of Conservation of Mass and the Law of Conservation of Energy are not really valid. Why not?

(Energy can be converted into mass and vice–versa.)

-----------------------------------------------------------------------------------------------------------------------------------------------c) State the law which replaces the Law of Conservation of Mass and the Law of Conservation of Energy. (The

Law of Conservation of Mass and Energy: The total of mass + energy does not change when areaction occurs.)

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■Binding Energy (continued)7d) Even though the Law of Conservation of Mass and the Law of Conservation of Energy are not really valid, we

were able to use them when considering chemical reactions without difficulty. Explain why. (The masschange which occurs when a chemical reaction occurs is so small that it cannot be measured even onthe best balance available. Therefore, the change can be ignored and chemists can pretend thatmass and energy are conserved separately.)

-----------------------------------------------------------------------------------------------------------------------------------------------e) State Einstein's equation which allows one to determine mass–energy equivalence. ( E = m*c2 or E = mc2)

-----------------------------------------------------------------------------------------------------------------------------------------------f) The energy associated with a change in the nucleus of a nuclide is generally very large. What is the energy unit

usually used when discussing binding energy? (MeV = megaelectron volts)

-----------------------------------------------------------------------------------------------------------------------------------------------g) The equation in e indicates that mass can be converted into energy and vice–versa. What is the conversion factor

between the two? (1 amu = 931 MeV)

-----------------------------------------------------------------------------------------------------------------------------------------------h) Define mass defect. (The difference between the mass of a nuclide and sum of the masses of the

electrons, protons, and neutrons which make up the nuclide.)

-----------------------------------------------------------------------------------------------------------------------------------------------i) Define binding energy. (The energy released when an atom is formed by combining protons, neutrons,

and electrons. It’s value can be obtained by converting the mass defect into energy using 1 amu =931 MeV.)

-----------------------------------------------------------------------------------------------------------------------------------------------j) Define nucleon. (p. A37 and p. 878)

-----------------------------------------------------------------------------------------------------------------------------------------------k) Define binding energy per nucleon. (p. 897)

-----------------------------------------------------------------------------------------------------------------------------------------------l) Chemists almost always calculate binding energy per nucleon rather than just binding energy. Why? (Binding

energy per nucleon can be used to compare the stability of various nuclides. Total binding energycannot.)

-----------------------------------------------------------------------------------------------------------------------------------------------m) Which group of nuclides tend to have the most binding energy per nucleon? I.E. Are the most stable? (Those

around iron. That is, those with about 30 neutrons and about 26 protons.)

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■Binding Energy (continued)7n) S. The binding energy per nucleon for a 6Li atom is 5.33 MeV/nucleon and the binding energy per nucleon for

a 60Ni atom is 8.74 MeV/nucleon. Which of the two nuclides is more stable?The higher the binding energy per nucleon, the more stable the nuclide. Therefore, a 60Ni atom is morestable than a 6Li atom.

-----------------------------------------------------------------------------------------------------------------------------------------------A. The binding energy per nucleon for a 25Mg atom is 8.22 MeV/nucleon and the binding energy per nucleon

for a 4He atom is 7.07 MeV/nucleon. Which of the two nuclides is more stable?

-----------------------------------------------------------------------------------------------------------------------------------------------B. The binding energy per nucleon for a 235U atom is 7.62 MeV/nucleon and the binding energy per nucleon

a 205At atom is 7.81 MeV/nucleon. Which of the two nuclides is more stable?

-----------------------------------------------------------------------------------------------------------------------------------------------C. The binding energy per nucleon for a 199Pb atom is 7.87 MeV/nucleon and the binding energy per nucleon

a 210Po atom is 5.74 MeV/nucleon. Which of the two nuclides is more stable?

-----------------------------------------------------------------------------------------------------------------------------------------------o) Perform the indicated calculation. For your information, the rest masses of the neutron, proton, and

electron are 1.0086650 amu, 1.0072765 amu, and 5.4858026*10-4 amu, respectively. (pp. 895-7)S. What is the binding energy per nucleon of 11B? Its atomic mass is 11.00656.

11B contains 5 p, 6 n, and 5 e- Mass defect (∆mass) = expected mass ...Therefore, - real massexpected mass = ∑(massp + massn + masse-) ∆mass = 11.091115 amu - 11.00656 amu == 5(1.0072765 amu) + 6(1.0086650 amu) + ∆mass = 0.0845554 amu

+ 5(5.4858026*10-4 amu) =

= 11.091115 amu BE = 0.0845554 amu( 931 MeV

1 amu ) =

R= 78.7210774 MeV = 78.7 MeV

& BE per nucleon = BE/(#p + #n) == (78.7 MeV)/(5 + 6) = 7.15 MeV/nucleon

-----------------------------------------------------------------------------------------------------------------------------------------------A. What is the binding energy per nucleon of 27Al? Its atomic mass is 26.97439.

-----------------------------------------------------------------------------------------------------------------------------------------------B. What is the binding energy per nucleon of 17O? Its atomic mass is 16.99474.

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■Binding Energy (continued)7(o)C. What is the binding energy per nucleon of 19F? Its atomic mass is 18.99346.

-----------------------------------------------------------------------------------------------------------------------------------------------D. What is the binding energy per nucleon of 13C? Its atomic mass is 13.00006.

-----------------------------------------------------------------------------------------------------------------------------------------------E. What is the binding energy per nucleon of 25Mg. Its atomic mass is 24.98584 amu.

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■Fission and Fusion8a) As you learned at the beginning of this module, the nuclei of radioactive elements can change by emitting a

variety of types of radiation. They can also change (or be changed) by undergoing fission or fusion.Distinguish between fission and fusion of nuclei. (p. 897)

-----------------------------------------------------------------------------------------------------------------------------------------------b) Give two places where fission occurs and two where fusion occurs. (Fission occurs in the atomic bomb or in a

nuclear power plant. Fusion occurs in the sun or in a hydrogen bomb.)•Two places where fission occurs:

•Two places where fusion occurs:

-----------------------------------------------------------------------------------------------------------------------------------------------c) Scientists are generally interested in fission or fusion as a means of producing energy. What general type of each

reaction is exothermic? (For fission reactions: Those in which large nuclei (those with mass numbersgreater than 130) break apart into smaller ones are exothermic. For fusion reactions: Those in whichsmall nuclei (those with mass numbers less than 15 or so) combine into a larger one are generallyexothermic. The most stable nuclides are those with mass numbers from 55-60.)•For fission reactions:

•For fusion reactions:

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■Fission and Fusion8d) Define critical mass. (The minimum amount of a fissionable substance needed to sustain fission.)

-----------------------------------------------------------------------------------------------------------------------------------------------e) Is the specified reaction an example of fission or fusion? Is it likely to be endothermic or exothermic? Explain.

S. 242Pu ➝ 142Ce + 100Kr-fission or fusion? |-endothermic or exothermic?Fission because a reactant nuclide is split | Process is exothermic because the fissioninto more than one smaller products. | of very large nuclides such as 242Pu is

| always exothermic.||

-----------------------------------------------------------------------------------------------------------------------------------------------A. He + H ➝ Li

-fission or fusion? |-endothermic or exothermic?|||||

----------------------------------------------------------------------------------------------------------------------------------------------- B. The uniting of two Cr atoms to form a single nucleus

-fission or fusion? |-endothermic or exothermic?|||||||

-----------------------------------------------------------------------------------------------------------------------------------------------C. The uniting of two Hf atoms to form a single nucleus.

-fission or fusion? |-endothermic or exothermic?||||||

-----------------------------------------------------------------------------------------------------------------------------------------------D. The breaking apart of a Th atom to form two other atoms of approximately equal mass


----------------------------------------------------------------------------------------------------------------------------------------------- E. The breaking apart of a P atom to form two other atoms of approximately equal mass


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✔✔✔■Kinetics of Radioactive Decay, Radioactive Dating9a) In Modules 12A and 12B you consider various aspects of rates of reaction. What kind of rate law best describes

radioactive decay? (p. 883)

-----------------------------------------------------------------------------------------------------------------------------------------------b) Define half-life. (p. 884)

-----------------------------------------------------------------------------------------------------------------------------------------------c) Write the integrated form of the first-order rate equation and the equation which relates rate constant to half-life.

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✔✔✔■Kinetics of Radioactive Decay, Radioactive Dating (continued)9d) The amount of radioactivity in old bones, rocks, etc. are often used to determine their age. This process is called

radioactive dating. One of the most important of the radioactive dating techniques is radiocarbon dating orcarbon-14 dating. Answer the following questions regarding it.•What is radiocarbon dating based on? (The radioactivity of 14C, an unstable isotope of carbon.)

•Carbon–14 is radioactive. How does it decay? (It decays by beta emission, 14C ➝ 14N + β- )

•What is the half–life of carbon–14? (5,730 years)

•The half–life of carbon–14 is relatively short compared to the age of the Earth, why then is there still enoughcarbon–14 on Earth to detect? (It is constantly produced by the reaction of high–energy neutrons withnitrogen in the atmosphere, 14N + n ➝ 14C + 1H ) .

•The amount of 14C in the earth’s atmosphere appears to be relatively constant. Why? (The radioactivedecay of the nuclide is in equilibrium with the reaction of high–energy neutrons with nitrogen to producethe nuclide. That is, the rate of its production is now equal to the rate at which it decays. )

•How does carbon–14 get into the tissues of living things? (Carbon-14, like other isotopes of carbon in theatmosphere, reacts with oxygen to form carbon dioxide. The carbon dioxide is then taken up byplants in photosynthesis and by animals when they eat plant life.)

•Carbon–14 in the tissues of living things is constantly decaying. Yet the ratio of carbon–14/carbon–12 inremains relatively constant while the thing is alive. Why? (The carbon–14 which decays is constantlybeing replaced by photosynthesis or eating plant life.)

•What happens to the amount of carbon–14 in the tissues of living things when they die? (There is no furtherreplacement of carbon-14 and the amount of carbon–14 in the living organism begins to decrease dueto radioactive decay. )

e) The amount of radioactivity in old bones, rocks, etc. are often used to determine their age. This process is calledradioactive dating. One of the most important of the radioactive dating techniques is radiocarbon dating orcarbon-14 dating. Answer the following questions regarding it.•The amount of carbon–14 (or ratio of carbon–14 to carbon–12) in a bone, a piece of wood, cloth, etc. today canbe used to estimate the age of the object using the equation in c above (ln (Xo/X) = kt) i f we make someassumptions about the process by which carbon–14 is produced and gets into living things. List three of thoseassumptions. (1. 14C is produced in the atmosphere at a relatively constant rate. 2. Carbon atomscirculate among the atmosphere, the ocean, and the living organisms at a rate very much faster thanthey decay. As a result, there is a constant concentration of 14C in living things. 3. After death,organisms no longer pick up 14C. )•1)

•2)

•3)

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✔✔✔■Kinetics of Radioactive Decay, Radioactive Dating (continued)9f) The percentage (or amount) of other radioactive elements in objects can also be used to estimate the age of those

objects if assumptions similar to those above for carbon-14 are made. List three such assumptions. i.e.Generalize on the assumptions above. (1. The amount of the radioactive nuclide present in similarsubstances when the object was formed is the same as it is today. 2. Atoms of the nuclide were ableto get into the object at a rate very much faster than they decay. 3. After the object was formed,there was no mechanism for the nuclei to enter nor leave the object.)•1)

•2)

•3)

-----------------------------------------------------------------------------------------------------------------------------------------------g) Work the following problems based on radioactive dating. (p. 891-2)

S. 40K decays to 40Ar with a half-life of 1.27*109 years. What is the age of a rock if 3.2 grams Ar and1.6 grams K are found at present. Assume there was no Ar at the beginning.This problem is just a special case of first-order reaction such as considered in Module 12A (#10).

Use ln ( XoX )= k*t, where k =

0.693t1/2

Therefore, ln ( 4.8 g1.6 )= 5.46*10-10 yr-1*time

For this problem, Xo = 3.2 + 1.6 g = 4.8 g ln 3.00 = 5.46*10-10 yr-1*time

since all 40Ar is assumed to have come from 1.10 = 5.46*10-10 yr-1*timethe decay of 40K, X = 1.6 g (amt. 40K left), time = 1.10/(5.46*10-10 yr-1) =and t1/2 = 1.27*109 years. = 2.0*109 years

So k = 0.693

1.27*109 years = 5.46*10-10 yr-1 So rock is 2.0*109 years old

-----------------------------------------------------------------------------------------------------------------------------------------------A. The decay of 14C to 14N has a half-life of 5,730 years. How old is a sample of human bone in which

carbon has 63.5% of the activity of similar bone taken from a cadaver today?

-----------------------------------------------------------------------------------------------------------------------------------------------B. 40K decays to 40Ar with a half-life of 1.27*109 years. What is the age of a rock in which the weight

ratio of 40Ar to 40K is 3.6?

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✔✔✔■Kinetics of Radioactive Decay, Radioactive Dating (continued)9g) Work the following problems based on radioactive dating. (p. 891-2)

C. The half–life of 210Pb is 21 years. What fraction of 210Pb would remain in a painting which is 312 yearsold if it were painted using a lead-based paint?

-----------------------------------------------------------------------------------------------------------------------------------------------D. 40K decays to 40Ar with a half-life of 1.27*109 years. What is the age of a rock in which the weight

ratio of 40Ar to 40K is 2.6?

-----------------------------------------------------------------------------------------------------------------------------------------------E. The decay of 14C to 14N has a half-life of 5,730 years. How old is a sample of bone in which

carbon has 43.5% of the activity of similar bone today?

-----------------------------------------------------------------------------------------------------------------------------------------------F. The half–life of 210Pb is 21 years. How old is a painting in which the activity of 210Pb activity is 0.17

as much as the activity as 210Pb in modern paint of a similar nature?

-----------------------------------------------------------------------------------------------------------------------------------------------G. A 21.3 gram sample of a radioactive nuclide decays to 9.22 grams in 44 minutes. What is the half–life of

the nuclide?

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✔✔✔■Kinetics of Radioactive Decay, Radioactive Dating (continued)9g) Work the following problems based on radioactive dating. (p. 891-2)

H. The half–life of a radioactive nuclide decays to is 36 hours. If you had 4.22 grams of the substance now,how much would remain after 57 hours have elapsed?

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■Biological Effects of Ionizing Radiation10a) Exposure to radiation can be harmful. For instance, excessive exposure to UV or x–rays can cause cancer. Is it

possible to live so as to totally eliminate exposure to radiation or radioactive nuclides?

-----------------------------------------------------------------------------------------------------------------------------------------------b) In modern America we frequently see articles in the newspaper or news magazines discussing controversies

regarding how much exposure to radiation is tolerable. Briefly state two such recent controversies.•

•

-----------------------------------------------------------------------------------------------------------------------------------------------c) There are a number of factors which must be taken into account when attempting to determining how much

damage a given type of radiation will do to living organisms. List four of those factors. (1. Energy. Thehigher the energy of the radiation, the more damaging it is to living organisms. Note: From 1010,you remember, of course, that gamma > x-rays > ultraviolet > visible > infrared > microwave > TV >FM radio > AM radio in terms of energy. 2. Penetrating ability: The more the radiation penetratesinto the body, the more damaging it is. 3. Ionizing ability: The more the radiation causes ionization,the more damaging it is. 4. The chemical properties of the radiation source: Substances which reactso as to form substances which are retained in the body are generally more harmful than those whichjust pass through.)Biological Factor Explanation of how each affects damage•

•

•

•

d) In an earlier portion of this module, you learned that the three primary types of radiation emitted by radioactivenuclides are alpha (α), beta (β-), and gamma (γ ) radiation. Indicate how each of these types of radiation vary ineach of the following: (1. Penetrating power: α < β- < γ ; 2. Ionizing ability: α > β- > γ )•Penetrating power:

•Ionizing ability:

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■Biological Effects of Ionizing Radiation (continued)10e) People who work in areas where there is danger of exposure to excessive ionizing radiation generally wear a

badge containing photographic film (or a similar device) which measures the amount of exposure they havereceived. In order to protect the safety of such workers, scientists for the federal government have developed astandard method for estimating the damage to the human body which will be caused by exposure to radiation.What are the two factors which are used estimating the damage by this method? (pp. 902-3)(1. Radiation absorbed dosage [rad], amount of energy deposited per kilogram of tissue. 2.Relative biological effectiveness of the radiation in causing damage [RBE], how the type of radiationaffects the body.)

Factor Acronym Brief description of each1)

2)

f) How are the two factors in e above combined to get an overall measure of the effect of ionizing radiation on thehuman body? (p. 1049) (rem = rad*RBE , rem which is short for Roentgen Equivalent for Man. )

-----------------------------------------------------------------------------------------------------------------------------------------------g) List two types of damage which radiation may cause in a living organism and briefly explain each. (p. 902)

(1. Genetic damage: Damage which does not affect the individual exposed but rather affects his/heroffspring. 2. Somatic damage: Damage done to the individual exposed.)-1)

-2)

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■Bonding/Model Act iv i ty to Improve Abi l i ty to Visual ize in 3-DA. a) Draw the Lewis structure of chlorite ion.

----------------------------------------------------------------------------------------------------------------------------------------------B. a) Draw the Lewis structure of sulfur trioxide.

----------------------------------------------------------------------------------------------------------------------------------------------C. a) Draw the Lewis structure of sulfur dioxide.

----------------------------------------------------------------------------------------------------------------------------------------------D. a) Draw the Lewis structure of phosphorous trichloride.

----------------------------------------------------------------------------------------------------------------------------------------------E. a) Draw the Lewis structure of chlorate ion.

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■Bonding/Model Activi ty to Improve Abil i ty to Visualize in 3-D (continued)F. a) Draw the Lewis structure of CH3NH2 (methyl amine).

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A-D b) Then use your model set to assemble a model of the species.

■Challenge Questions

Predict which is more stable and explain your prediction:(The rest masses of the neutron, proton, and electron are 1.0086650 amu, 1.0072765 amu, and 5.4858026*10-4

amu, respectively.)

A.. Four protons, four neutrons and four electrons organized as two 4He atoms or as one 8Be atom.(Atomic masses: 4He: 4.0026033 amu; 8Be: 8.0053052 amu)

B. Sixteen protons, sixteen neutrons and sixteen electrons organized as two 16O atoms or as one 32S atom.(Atomic masses: 16O: 15.9949146 amu; 32S: 31.972072 amu)

C. Six protons, six neutrons and six electrons organized as three 4He atoms or as one 12C atom.(Atomic masses: 4He: 4.0026033 amu; 12C: 12.000000 amu)

D. Twelve protons, twelve neutrons and twelve electrons organized as two 12C atoms or as one 24Mg atom.(Atomic masses: 24Mg: 23.985045 amu; 12C: 12.000000 amu)

E. Six protons, eight neutrons and six electrons organized as two 7Li atoms or as one 14C atom.(Atomic masses: 7Li: 7.016005 amu; 14C: 14.003242 amu)



Revised by Ann Privett, Spring, 1997; Ann Privett, Spring, 2000; Ann Privett, Spring, 2001


Study Guide for Module 18—Nuclear Chemistry Assignment: Chapter 18 in Chemistry, ... Structure of...

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